For each a [is an element of the set] (0, 1/2), there exists a random measure [beta] [subscript] a which is supported on the set of points where two-dimensional Brownian motion spends a units of local time. The measure ...

A prismatoid is a polyhedron with all vertices in two parallel planes. A polyhedron P is isogonal if all its vertices form one transitivity class under isometric symmetries of P. Although these restrictions appear very ...

My original set of lectures on Mechanics was divided into three parts: Lagrangian Mechanics, Hamiltonian Mechanics, Equivariant Mechanics. The present text is an order of magnitude expansion of the first part and is ...

We consider a stochastic flow in which individual particles follow skew Brownian motions, with each one of these processes driven by the same Brownian motion. One does not have uniqueness for the solutions of the corresponding ...

We investigate when an upper bound on expected lifetimes of conditioned diffusions associated with elliptic operators in divergence and non-divergence form can be found. The critical value of the parameter is found for ...

We define a local time flow of skew Brownian motions, i.e., a family of solutions to the stochastic differential equation defining the skew Brownian motion, starting from different points but driven by the same Brownian ...

The Martin boundary with respect to the Laplacian and with respect to uniformly elliptic operators in divergence form can be identified with the Euclidean
boundary in C [to the power of gamma] domains, where [gamma](x) = ...

The system for publishing mathematical articles should be reformed and the new system should resemble, on the economic side, the bottled water industry. My main theses are: (i) the results of the mathematical research ...

These notes can serve as a mathematical supplement to the standard graduate level texts on general relativity and are suitable for self-study. The exposition is detailed and includes accounts of several topics of current ...

We investigate the number N of molecules needed to perform independent diffusions in order to achieve bonding of a single molecule to a specific site in time t [subscript] 0. For a certain range of values of t [subscript] ...

Let f be an analytic function defined on D [is a subset of] [complex numbers] C. If [the derivative of the function f at the point x] has a limit
when [the set] x [into the set] z [is an element of the set partial derivative] ...

This is a review of research on geometric properties of Neumann eigenfunctions related to the "hot spots" conjecture of Jeff Rauch. The paper also presents, in an informal way, some probabilistic techniques used in the proofs.